The Antonov problem for rotating systems

TL;DR

This paper investigates the effects of rotation on the classical Antonov problem, revealing a critical angular momentum that alters the system's equilibrium phases and prevents the Antonov limit in highly rotating regimes.

Contribution

It introduces the analysis of rotational effects in the Antonov problem, identifying a critical angular momentum and describing the resulting phase behavior and stability.

Findings

Existence of a critical angular momentum $\lambda_c$ affecting system phases.

High rotation leads to binary star formation at low energies.

No Antonov limit for $\lambda>\lambda_c$.

Abstract

We study the classical Antonov problem (of retrieving the statistical equilibrium properties of a self-gravitating gas of classical particles obeying Boltzmann statistics in space and confined in a spherical box) for a rotating system. It is shown that a critical angular momentum $\lambda_c$ (or, in the canonical language, a critical angular velocity $\omega_c$) exists, such that for $\lambda<\lambda_c$ the system's behaviour is qualitatively similar to that of a non-rotating gas, with a high energy disordered phase and a low energy collapsed phase ending with Antonov's limit, below which there is no equilibrium state. For $\lambda>\lambda_c$, instead, the low-energy phase is characterized by the formation of two dense clusters (a ``binary star''). Remarkably, no Antonov limit is found for $\lambda>\lambda_c$. The thermodynamics of the system (phase diagram, caloric curves, local stability) is analyzed and compared with the recently-obtained picture emerging from a different type of statistics which forbids particle overlapping.